Problem: Simplify the following expression: ${-2(5-2k)+2(-5k+1)}$
Distribute the ${-2}$ into the first set of parentheses: $ {-2(}\gray{5-2k}{)} + 2(-5k+1) $ $ {-10+4k} + 2(-5k+1) $ Distribute the ${2}$ into the parentheses: $ -10+4k + {2(}\gray{-5k+1}{)} $ $ -10+4k {-10k+2} $ Rewrite the expression to group the ${k}$ terms and numeric terms: $ {4k - 10k} {-10 + 2}$ Combine the ${k}$ terms: $ {-6k} {-10 + 2}$ Combine the numeric terms: $ {-6k} {-8}$ The simplified expression is $-6k-8$